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<p>Handling missing data in complex multivariate datasets remains a critical challenge in geostatistical modeling. This paper introduces a hybrid approach for multiple imputation that integrates machine learning (ML) regression models with the multivariate Gaussian (MG) paradigm to construct conditional distributions. The methodology leverages the predictive capacity of ML algorithms to estimate conditional means, while using a calibrated variance derived from an estimated parameter obtained through accuracy plots. To incorporate spatial structure, the framework adopts a Bayesian updating scheme in which the prior distribution is obtained from simple kriging and the likelihood from the ML–MG model. The result is a posterior distribution that reflects both spatial continuity and multivariate relationships. The workflow follows a sequential path to impute missing values, where each previously simulated value is used for conditioning subsequent ones. A series of realizations is generated, enabling uncertainty modeling and ensuring compatibility with a geostatistical simulation workflow. A dataset exhibiting nonlinear and heteroscedastic relationships is used to demonstrate the method. An example from a nickel deposit is also used to illustrate its applicability in realistic mining settings, including geometallurgical datasets where a clear primary-response relationship between variables exists. The approach is shown to produce reliable imputations from univariate, bivariate, and spatial perspectives, even in the presence of substantial missing data.</p>

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A Hybrid Approach to Multiple Imputation for Geological and Geometallurgical Datasets Using Machine Learning Regression and the Multivariate Gaussian Distribution

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Gabriel de Castro Moreira,
  • João Felipe Coimbra Leite Costa,
  • Clayton V. Deutsch

摘要

Handling missing data in complex multivariate datasets remains a critical challenge in geostatistical modeling. This paper introduces a hybrid approach for multiple imputation that integrates machine learning (ML) regression models with the multivariate Gaussian (MG) paradigm to construct conditional distributions. The methodology leverages the predictive capacity of ML algorithms to estimate conditional means, while using a calibrated variance derived from an estimated parameter obtained through accuracy plots. To incorporate spatial structure, the framework adopts a Bayesian updating scheme in which the prior distribution is obtained from simple kriging and the likelihood from the ML–MG model. The result is a posterior distribution that reflects both spatial continuity and multivariate relationships. The workflow follows a sequential path to impute missing values, where each previously simulated value is used for conditioning subsequent ones. A series of realizations is generated, enabling uncertainty modeling and ensuring compatibility with a geostatistical simulation workflow. A dataset exhibiting nonlinear and heteroscedastic relationships is used to demonstrate the method. An example from a nickel deposit is also used to illustrate its applicability in realistic mining settings, including geometallurgical datasets where a clear primary-response relationship between variables exists. The approach is shown to produce reliable imputations from univariate, bivariate, and spatial perspectives, even in the presence of substantial missing data.